摘要
基于求线性矩阵方程约束解的修正共轭梯度法的基本思想,研究在最优控制系统中遇到的离散时间代数Riccati矩阵方程(DTARME)对称解的数值计算问题.首先对DTARME中的逆矩阵采用矩阵级数方法进行等价转化,然后运用牛顿算法将DTARME的对称解问题转化为线性矩阵方程的对称解或者对称最小二乘解问题,最后采用修正共轭梯度法进行计算.由此,可建立求DTARME的对称解的双迭代算法,并给出相应的收敛性结论.数值算例表明,双迭代算法是有效的.
Based on the modified conjugate gradient method in computing constrained solution of general linear matrix equation,an iterative method is proposed to compute the symmetric solution of discrete time algebra Riccati matrix equation(DTARME) in optimal control system.Firstly,DTARME is processed by matrix series.Then Newton's method is applied to find symmetric solution of DTARME,and the symmetric solution or symmetric least-square solution of the linear matrix equation is solved.Finally,the modified conjugate gradient method is applied to solve the derived linear matrix equation.Therefore,a double iterative method is established to find symmetric solution of DTARME,and the corresponding convergence conclusion is given.Finally,numerical experiments show that the double iterative algorithm is effective.
出处
《系统科学与数学》
CSCD
北大核心
2013年第12期1415-1422,共8页
Journal of Systems Science and Mathematical Sciences
基金
国家自然科学基金(11071196)资助课题
关键词
DTARME
对称解
牛顿算法
修正共轭梯度法
双迭代算法
DTARME
symmetric solution
Newton's method
modified conjugate gradient method
double iterative algorithm.